Difference between revisions of "2021 AIME I Problems/Problem 14"
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==Problem== | ==Problem== | ||
| − | + | For any positive integer <math>a,</math> <math>\sigma(a)</math> denotes the sum of the positive integer divisors of <math>a</math>. Let <math>n</math> be the least positive integer such that <math>\sigma(a^n)-1</math> is divisible by <math>2021</math> for all positive integers <math>a</math>. Find the sum of the prime factors in the prime factorization of <math>n</math>. | |
==Solution== | ==Solution== | ||
Revision as of 15:50, 11 March 2021
Problem
For any positive integer 
denotes the sum of the positive integer divisors of 
. Let 
be the least positive integer such that 
is divisible by 
for all positive integers . Find the sum of the prime factors in the prime factorization of .
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
